The armed group attacked the pro-government fighters in Baghlan on Friday night, Afghan officials said. Eight others were wounded in the hours-long fighting late on Friday.
The Taliban claimed responsibility for the attack in a statement.
New round of talks between the US and the Taliban has began in Doha on Saturday, just days after US Secretary of State Mike Pompeo said Washington is hoping for an Afghan peace agreement before September 1.
“There is a genuine sense of expectation on both sides,” a senior US official, who declined to be identified as he was not authorised to speak to media, told Reuters news agency.
“It’s a make-or-break moment.”
The Doha talks centre on four interconnected issues: a Taliban guarantee that it will not allow fighters to use Afghanistan to launch international attacks, the withdrawal of US and NATO forces, an intra-Afghan dialogue and a permanent ceasefire.
About 20,000 foreign troops, most of them American, are in Afghanistan as part of a US-led NATO mission to train, assist and advise Afghan forces. Several thousand US forces carry out counterterrorism operations.
Khalilzad has been in Afghanistan and regional countries for several weeks meeting their representatives and Afghan officials, including President Ashraf Ghani.
On a trip to Kabul on Tuesday, US Secretary of State Mike Pompeo said the US was close to finishing a draft agreement with the group on counterterrorism assurances and he hoped a peace pact could be reached by September 1.
The pace of talks between the US and Taliban has sped up as Afghanistan heads for presidential elections on September 28.
“This is one of the crucial meetings,” a senior Taliban leader in Qatar said, on condition of anonymity.
“If we fail to find any solution to the Afghan conflict then we would like to negotiate with the elected representatives of the American people.”
The Taliban has repeatedly refused to allow representatives of the Afghan government join the negotiations, but has held several rounds of talks with some Afghans, including former President Hamid Karzai, in two meetings in Moscow earlier this year.
The Taliban, which controls or contests half the country, more than at any time since being overthrown by the US invasion in 2001, does not support the election process and has rejected a ceasefire.
Ghani, who has been sidelined from the talks, hopes the seventh round will open the door for an intra-Afghan meeting.
Civil society representatives, especially women’s groups are concerned that a deal with the Taliban, which banned women from many aspects of public life while in power, will roll back freedoms they have gained since the group was removed from power in 2001.